Question

$$ for $a$ and $b$ real numbers, can the function given ever be a continuous function? II so, specify the value for $a$ and $b$ that would make it so. $$f(x)=\left\{\begin{array}{ll} a x & x \leq 2 \\ b x^{2} & x>2 \end{array}\right.$$

          $$ for $a$ and $b$ real numbers, can the function given ever be a continuous function? II so, specify the value for $a$ and $b$ that would make it so.
$$f(x)=\left\{\begin{array}{ll}
a x & x \leq 2 \\
b x^{2} & x>2
\end{array}\right.$$

Added by Jonathan B.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Rebecca Belvin

Step 1

To do this, we need to check if the left-hand limit and the right-hand limit of the function at $x=2$ exist and are equal. The left-hand limit is given by $\lim_{x\to 2^-} f(x) = \lim_{x\to 2^-} ax = 2a$. The right-hand limit is given by $\lim_{x\to 2^+} f(x) Show more…

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$$ for $a$ and $b$ real numbers, can the function given ever be a continuous function? II so, specify the value for $a$ and $b$ that would make it so. $$f(x)=\left\{\begin{array}{ll} a x & x \leq 2 \\ b x^{2} & x>2 \end{array}\right.$$